Interest Rate

Interest Rate in Health Economic Appraisal

An interest rate is a price, the price of moving purchasing power through time, stated as the yearly share of a loan that the borrower pays the lender on top of the sum borrowed. A health board that borrows GBP 100 today at 5% repays GBP 105 a year later, so the extra GBP 5 is what having the money a year earlier costs. Health economists meet the idea whenever costs and benefits fall in different years, because the return that money can earn in the market is one benchmark for what a delayed gain is worth. The interest rate and the discount rate used in an economic evaluation are close relatives, and much of the welfare economics of discounting asks when a market rate can stand in for the social rate.

The interest rate as the price of time

The CORE textbook The Economy defines the interest rate as the price of bringing buying power forward in time. A borrower receives a principal now and later repays the principal plus interest, so the rate can be read off any loan once the two sums are known.

$$r = \frac{R}{P} - 1$$

where $r$ is the annual interest rate, $R$ is the repayment due one year later and $P$ is the principal received now. In the CORE example a borrower who receives 91 now and repays 100 a year later pays $\frac{100}{91} - 1 \approx 0.10$, a rate of 10%.

CORE describes one plus the interest rate as the marginal rate of transformation between future and present goods, since one more unit now costs one plus $r$ units later. The survey of social discount rates by Zhuang and colleagues for the Asian Development Bank describes the capital market as clearing at the interest rate that equates the supply of and demand for investible funds. Many rates coexist in practice. CORE explains that a central bank sets a policy rate and that commercial banks lend to households and firms at a higher rate, the difference being a markup or spread.

Why a perfect capital market links impatience and the return on capital

The welfare meaning of the interest rate comes from what people do when they can borrow and lend freely. CORE shows a borrower bringing consumption forward until the slope of her indifference curve, her marginal rate of substitution between consumption now and later, equals the slope of the feasible frontier set by the market.

$$1 + \rho = 1 + r$$

where $\rho$ is the person's discount rate, defined by CORE as the slope of the indifference curve minus one, and $r$ is the interest rate. At the chosen point the person's discount rate equals the rate of interest, and CORE traces that discount rate to a wish to smooth consumption and to pure impatience, which ties the market rate to time preference.

Zhuang and colleagues extend the argument to the whole economy. In a perfectly competitive economy without distortions, the social rate of time preference of savers and the social opportunity cost of capital, the return that displaced private investment would have earned, both equal the market interest rate, which is then the appropriate social discount rate for an efficient allocation of resources. In that textbook case a health ministry could use the rate on a riskless loan to weigh a vaccination programme whose costs fall now and whose savings arrive years later.

Taxes and other wedges between saving and investing

Real capital markets do not meet those conditions, and the gap matters for cost-benefit analysis. Zhuang and colleagues name taxes on corporate income and on interest earnings as a typical distortion, along with risk, information asymmetry and externalities. These create a wedge between the social rate of time preference and the social opportunity cost of capital, with the former generally lower, and push both away from the market interest rate.

Once the wedge exists, no single market rate measures the cost of public funds. The HM Treasury supplementary guidance on discounting describes two broad approaches. A social time preference approach reflects the rate at which society is willing to trade consumption today for consumption tomorrow, and a social opportunity cost of capital approach reflects the cost of government funding and the return on the private investment it displaces. A health programme whose funding crowds out private investment carries the opportunity cost of that investment, while one paid for by reduced consumption carries the time preference cost.

How UK appraisal uses market interest rates

The Green Book supplementary guidance on discounting, updated in October 2026, sets the Social Time Preference Rate (STPR) at 3.00% in real terms for years 1 to 30 of a proposal, 2.50% for years 31 to 75 and 2.25% for years 76 to 125. The STPR comes mainly from the Ramsey formula, but HM Treasury triangulates the risk-free part with other evidence, including inflation-adjusted yields on government bonds, and the guidance reports that in June 2026 real yields on 10-year, 20-year and 40-year gilts were around 2%. After triangulation the Ramsey estimate of 1.875% is raised by 0.125 percentage points to 2.00%, and a systematic risk premium of 1.00% is added to give 3.00%.

The Green Book (2026) notes that the government typically pays interest on its borrowing and states that these costs of raising public funds should not generally be included in appraisal, because most proposals are funded from pre-determined departmental budgets. Private finance is the exception. The Green Book states that private finance usually costs more than government borrowing, and when a shortlist holds both a private finance option and a public sector option, the costs of every option must also be discounted at the risk-free, real-terms gilt rate that most closely matches the weighted average duration of the contract. That sensitivity analysis brings the government's own borrowing rate into the comparison, as it would for a hospital building procured through private finance.

For health technology assessment the NICE manual (PMG36), last updated on 13 October 2026, asks for costs and health effects to be discounted at the same rate of 3.5% a year in the reference case, with analyses at 1.5% allowed alongside in specific circumstances. Because the manual fixes that rate, an analysis for NICE uses 3.5% whatever market interest rates are when the model is built.

Nominal and real interest rates

The rate quoted by a bank is nominal, uncorrected for inflation. CORE defines the real interest rate as the nominal rate minus inflation, the Fisher equation, so a 10% loan repaid after prices rise 6% earns a real 4%. The subtraction is an approximation, and the exact relation multiplies growth factors.

$$(1 + i) = (1 + r)(1 + \pi)$$

where $i$ is the nominal interest rate, $r$ is the real interest rate and $\pi$ is the inflation rate, all per year. The Green Book follows this structure. The STPR is a real rate to be applied only to values in real terms, so general inflation is removed first with the GDP deflator, and the guidance warns that adding the inflation rate to the discount rate gives a mathematically incorrect result. In its Table 8, with 2% inflation, the year 1 deflator factor of 0.9804 times the discount factor of 0.9709 gives about 0.9519, the same as one nominal discount at 1.0506, a rate of 5.06% and not 5%. The time value of money page treats price adjustment more fully.

Worked example with a tax wedge and a prevention programme

The figures are illustrative. A riskless loan pays a nominal 6% a year, inflation is 2% a year, and savers pay a 25% tax on interest income. Before tax, investment earns a real return of

$$\frac{1.06}{1.02} - 1 \approx 0.0392$$

where 1.06 is one plus the nominal rate and 1.02 is one plus inflation, about 3.92%, a proxy for the real opportunity cost of capital. After tax, savers keep 0.06 × 0.75 = 0.045, a nominal 4.5%, and their real return is

$$\frac{1.045}{1.02} - 1 \approx 0.0245$$

where 1.045 is one plus the after-tax nominal rate, about 2.45%, a proxy for the real rate of time preference. The tax opens a wedge of about 1.47 percentage points.

A local authority vaccination programme costs GBP 1,000,000 now and saves GBP 1,180,000 in real terms in health and social care costs in year 5. The present value of the saving is

$$PV = \frac{B}{(1 + r)^{t}}$$

where $B$ is the real saving, $r$ is the real discount rate and $t$ is the number of years until the saving arrives.

Growth factors use the unrounded rates 1.045/1.02 and 1.06/1.02. At 3.00% the growth factor is 1.03 to the fifth power, about 1.15927, so the present value is $\frac{1180000}{1.15927} \approx 1017878$ and the net present value is about GBP 17,878. The programme's internal rate of return, the fifth root of 1.18 less one, is about 3.37%, so it passes at any rate below that. The programme is worth doing if its funds come from consumption and not if they displace private investment earning the pre-tax return, which is why the welfare economics of the interest rate turns on where the money comes from.

Interest charges inside health care unit costs

The interest rate also appears, as the cost of tying up money, inside the unit costs used in UK models. The Unit Costs of Health and Social Care 2025 manual reports NHS wheelchair capital values depreciated over five years at a 3.5% discount rate, the expected life of a new chair. For the low-need equipment package the capital value is GBP 411 and the reported unit cost is GBP 91, which the annuity factor reproduces.

$$A = \frac{1 - 1.035^{-5}}{0.035} \approx 4.5151$$

where $A$ is the five-year annuity factor at 3.5%, so that $\frac{411}{4.5151} \approx 91.03$, the yearly charge whose present value over five years equals the purchase price. The capital cost page sets out the equivalent annual cost method in full.

The interest rate in the welfarist and extra-welfarist debate

In welfarist cost-benefit analysis the interest rate matters because, in an ideal market, it measures what people would give up in consumption to receive benefits sooner, and welfare economics asks whether that market valuation should be the social one. Attema, Brouwer and Claxton, reviewing discounting in economic evaluation, illustrate the opportunity cost reason for discounting with money placed in a riskless government bond at 2%, and note that equal discounting has long rested on the Ramsey equation or on riskless returns on government bonds.

The same review shows the market rate losing its direct role when the health budget is fixed. If new spending must displace other health care, the opportunity cost is the expected health forgone, and the relevant return is the health that marginal NHS spending produces, the idea behind a cost-effectiveness threshold based on health opportunity cost. That setting fits the extra-welfarist aim of maximising health from a set budget. Across decision contexts the authors conclude that discount rates depend heavily on how the marginal productivity of health spending and the consumption value of health develop over time. They note that the need to allow for a growing value of health holds whether the social welfare function is welfarist or extra-welfarist, and the case for differential discounting grows out of that argument.

Where the interest rate stops and neighbouring ideas begin

The interest rate is an observed market price, while the discount rate is a value set for appraisal, usually by guidance such as PMG36 or the Green Book. The social discount rate is the rate a government sets for public appraisal, such as the Green Book STPR, and the social opportunity cost of capital is one reading of what that rate should be. Discount factors and annuity factors are computed from a rate, and the internal rate of return is the rate at which net present value is zero. The present value and discounting pages cover the shared mechanics.

Common misreadings of interest rates in appraisal

A common error treats today's Bank of England or gilt rate as the discount rate for a health appraisal. The Green Book uses gilt yields only to triangulate its STPR and the NICE manual fixes its own rate, so a market movement changes neither required rate until the guidance is revised.

Another error mixes real and nominal values, such as cash-terms costs discounted at a real rate, or treats the sum of inflation and the real rate as exact. Deflating first and discounting second, as the Green Book requires, avoids both problems.

Counting interest twice is a further mistake. Where capital is annuitised or a cost stream is discounted, the time cost of money is already included, and adding loan interest as a cost charges for it again, which matches the Green Book exclusion of the costs of raising public funds outside private finance.

Sources

• Attema AE, Brouwer WBF, Claxton K. Discounting in economic evaluations. PharmacoEconomics. 2018;36(7):745-758. https://doi.org/10.1007/s40273-018-0672-z
• CORE Team. The Economy 1.0. CORE Econ; 2017. Units 10 and 15. https://books.core-econ.org/the-economy-v1/book/text/10.html
• HM Treasury. The Green Book (2026). Updated 28 October 2026. Including Annex A, Private finance models. https://www.gov.uk/government/publications/the-green-book--2/the-green-book-2026
• HM Treasury. Green Book supplementary guidance: discounting. October 2026. https://www.gov.uk/government/publications/green-book-supplementary-guidance-discounting
• Jones K, Weatherly H, Barker A, et al. Unit Costs of Health and Social Care 2025 Manual. Care and Outcomes Research Centre, University of Kent, and Centre for Health Economics, University of York; 2026. Section 6.3, NHS wheelchairs. https://kar.kent.ac.uk/115569/
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Section 4.5, Discounting. https://www.nice.org.uk/process/pmg36
• Zhuang J, Liang Z, Lin T, De Guzman F. Theory and Practice in the Choice of Social Discount Rate for Cost-Benefit Analysis: A Survey. ERD Working Paper 94. Asian Development Bank; 2007. https://www.adb.org/sites/default/files/publication/28360/wp094.pdf